Description

This course is meant for biologists who want to learn mathematical
principles relevant to current biological research. About half of the
course covers topics on information theory, inference, statistics, and
probabilistic modeling. The second half of the course covers dynamical
systems in biology, including random walks, feedback control, and
molecular population dynamics.

Each week-long unit is devoted to one specific topic, and is based in
one or more scientific papers selected from the recent literature.
Each unit includes a set of lectures (available online), a practical
session, and a homework. The practical session follows a flipped-class
model in which students work in the classroom implementing the methods
described in the lecture.

Aims and objectives

I will show you how to be critical with your data; and how to run the
right control experiments. This course covers some of the mathematical
tools to do that. I will use plain language as much as possible
without losing mathematical rigor. I want to get across to you that
you should not use statistical tests for which you do not understand
the assumptions (and they all have them!), nor treat math as a black
box. And if your calculus fails you and cannot find an analytic
expression, then you can solve a problem numerically.

I also would like to show you that doing simple scripting is easy, and
that in doing so, you can stop making assumptions about how simple
models work, and instead see how they work. The course has an
important emphasis on computational work. Computer literacy is
fundamental for experimental biologists. You are expected to know
some basics of one computer language of choice (Matlab, Python, Perl,
or others), but you are not expected to be an expert on any one of
them. By the end of the course, hopefully you will be confident
launching into your own computational approaches to data
collection, data analysis, and model testing.

There. Let’s get started!

Prerequisites and background

If you are a Molecular, Cells and Organisms (MCO) graduate student
taking the course, you will be instructed to take a minicourse in
mathematics in early January, followed by a qualifying exam.
Otherwise, you would need a taste for mathematics applied to biology,
and an interests (and hopefully a bit of previous experience) in
coding.

We expect to have most students coding in Matlab, because it seems to
be the default language that biologist feel they must learn (not sure
why), but if you know python or want to use this course as an excuse
to learn python, you are encouraged to do so. That is what I plan to
do, although my default scripting tool is perl.

Policies, expectations, grading

There will be one homework per week, and one final exam (open
book). Grade will be based on homework (60%), final exam (30%), and
participation (10%).

Materials

The following materials are for reference. You are not expected to get
them all, not even one of them. The class notes should contain all
materials covered in this course; and specific reading materials will
be proposed with each topic. The books will for you on reserve in the
Cabot library so you can look at them. One of the books (MacKay’s–one
of the most insightful books ever, but not super easy to read) is free
online.

For the first half of the course, I will use materials from these books:

It is cheap, and it includes most of the mathematical expressions I
need on a day-to-day basis for integrals, series, special functions,
etc. And you can also find the pdf of the whole book online
(here).

Academic integrity

You must do each week’s project individually, on your own, rather than
working collaboratively in groups. Your writing and your code must be
your original work.

Meanwhile, you are free to talk with each other, and to consult any
resource, and to study code from other sources.

Accommodations for students with disabilities

Students needing accommodations because of a disability should present
their Faculty Letter from the Accessible Education Office (AEO) and
speak with an instructor by the end of the second week of the term for
us to be able to respond in a timely manner.